In the expression |*a*:*sxy*,*b*:*SXY*|, "*a*" and "*b*" are numbers for fundamental
matrices which are listed in the following part. The numbers (*x*,*y*)
and (*X*,*Y*) mean the displacements of the elements. Therefore,
the matrix element for *a*:*xy* is given by
such that is one of
fundamental matrix.
*s* and *S* mean symmetrical transformations summarized in the following table.

For example, the matrix element for *a*:3*xy* is an
element
of a fundamental matrix.
The above symmetrical transformations cover of symmetries.
These results are calculated by the
awk script.
Prof. Suzuki's "ultra-super" magic squares are also decomposed,
which leads to only two fundamental digit-matrices
(here).